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Добірка наукової літератури з теми "Smooth numbers"

Автор: Grafiati

Опубліковано: 29 березня 2025

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Статті в журналах з теми "Smooth numbers"

1

Baker, Roger. "Smooth numbers in Beatty sequences." Acta Arithmetica 200, no. 4 (2021): 429–38. http://dx.doi.org/10.4064/aa210322-22-6.

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2

Laishram, Shanta, and M. Ram Murty. "Grimm's conjecture and smooth numbers." Michigan Mathematical Journal 61, no. 1 (March 2012): 151–60. http://dx.doi.org/10.1307/mmj/1331222852.

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3

Oehring, Charles. "Singular numbers of smooth kernels." Mathematical Proceedings of the Cambridge Philosophical Society 103, no. 3 (May 1988): 511–14. http://dx.doi.org/10.1017/s0305004100065129.

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In [12] we elaborate the vague principle that the behaviour at infinity of the decreasing sequence of singular numbers sn(K) of a Hilbert–Schmidt kernel K is at least as good as that of the sequence {n−1/qω(n−1;K)}, where ωp is an Lp-modulus of continuity of K and q = p/(p − 1), where 1 ≤ p ≤ 2. Despite the author's effort to justify his study of refinements of the half-century old theorem of Smithies [13], that theorem remains the central result of the subject (viz. that for 0 < a ≤ 1, K∈Lip(a, p) implies that sn(K) = O(n−α−1/q)). For example, Cochran's omnibus theorems [5, 6] that delimit the Schatten classes to which a kernel belongs are based on the blending of ‘smoothness’ conditions and emphasize the pivotal role of the principal corollary of Smithies' theorem (viz. {sn}∈lr if r−1 < α + q−1). Cochran later offered in [7] a very simple derivation of the corollary from a Fourier series theorem of Konyushkov (see [2], vol. II, p. 197), whose proof was, however, at least as intricate as Smithies' demonstration.

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4

Qin, Zhenzhen, and Tianping Zhang. "Kloosterman sums over smooth numbers." Journal of Number Theory 182 (January 2018): 221–35. http://dx.doi.org/10.1016/j.jnt.2017.06.011.

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5

CROOT, ERNIE. "SMOOTH NUMBERS IN SHORT INTERVALS." International Journal of Number Theory 03, no. 01 (March 2007): 159–69. http://dx.doi.org/10.1142/s1793042107000833.

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We show that for any ∊ > 0, there exists c > 0, such that for all x sufficiently large, there are x1/2 ( log x)- log 4 - o(1) integers [Formula: see text], all of whose prime factors are [Formula: see text].

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6

Shparlinski, Igor E. "Character sums with smooth numbers." Archiv der Mathematik 110, no. 5 (March 5, 2018): 467–76. http://dx.doi.org/10.1007/s00013-018-1168-y.

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7

kinsley, Anto A., and J. Joan princiya. "Center Smooth Sets and Center Smooth Numbers of Graphs." Journal of Physics: Conference Series 1770, no. 1 (March 1, 2021): 012071. http://dx.doi.org/10.1088/1742-6596/1770/1/012071.

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8

Heath-Brown, D. R. "The differences between consecutive smooth numbers." Acta Arithmetica 184, no. 3 (2018): 267–85. http://dx.doi.org/10.4064/aa170913-11-7.

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9

Shparlinski, Igor E. "Character sums over shifted smooth numbers." Proceedings of the American Mathematical Society 135, no. 09 (May 2, 2007): 2699–706. http://dx.doi.org/10.1090/s0002-9939-07-08785-0.

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10

Oehring, Charles. "Singular numbers of smooth kernels. II." Mathematical Proceedings of the Cambridge Philosophical Society 105, no. 1 (January 1989): 165–67. http://dx.doi.org/10.1017/s0305004100001493.

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Reade[10] has recently improved Weyl's classical estimate λn = o(n−3/2) for the eigenvalues of a symmetric kernel K∈C1 by relaxing the Cl hypothesis to the assumptions that K∈L2[0, 2π]2, that K is absolutely continuous in each variable separately, and that both ∂K/∂s and ∂K/t belong to L2[0, 2π]2. The conclusion of his theorem, that is, of course, stronger than λn = o(n−3/2).

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Дисертації з теми "Smooth numbers"

1

Moore, Daniel Ross. "An Intrinsic Theory of Smooth Automorphic Representations." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1524174589105537.

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2

Mansour-Tehrani, Mehrdad. "Spacial distribution and scaling of bursting events in boundary layer turbulence over smooth and rough surfaces." Thesis, University College London (University of London), 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.261297.

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3

Symes, Joseph Alexander. "Dry inclined galloping of smooth circular cables in the critical reynolds number range." Thesis, University of Bristol, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.546204.

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4

Fahrner, Anne-Kathrin [Verfasser], and Jürgen [Akademischer Betreuer] Hausen. "Smooth Mori dream spaces of small Picard number / Anne-Kathrin Fahrner ; Betreuer: Jürgen Hausen." Tübingen : Universitätsbibliothek Tübingen, 2017. http://d-nb.info/1196703264/34.

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5

Zouari, Hichem. "Les entiers friables sous contraintes digitales." Electronic Thesis or Diss., Université de Lorraine, 2024. http://www.theses.fr/2024LORR0255.

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Cette thèse aborde plusieurs questions liées à la fonction somme des chiffres et aux entiers friables. Le premier chapitre est consacré à une introduction qui rassemble les origines des thèmes principaux abordés dans cette thèse, ainsi que les rappels théoriques et les notations nécessaires pour la suite du travail. Les principaux résultats obtenus au cours de cette recherche y seront également présentés. Le deuxième chapitre est consacré à l'étude des propriétés de l'ensemble ({ n leq x : n ext{ est } k ext{-libre}, , s_q(Q(n)) equiv a pmod{m} }), où ( a in mathbb{Z} ), ( k ), et ( m ) désignent des entiers naturels supérieurs ou égaux à 2. La fonction ( s_q ) représente la somme des chiffres en base ( q ), les entiers ( k )-libres sont ceux qui ne sont pas divisibles par la ( k )-ième puissance d'un nombre premier, et ( Q ) est un polynôme de degré supérieur ou égal à 2. Afin de montrer notre résultat principal, nous évaluons des sommes exponentielles du type (sum_{n leq x atop{ n ext{ est } k ext{-libre}}} e(alpha s_q(Q(n)))), où ( alpha ) est tel que ((q - 1)alpha in mathbb{R} setminus mathbb{Z}). À la fin, nous montrons un résultat d'équirépartition modulo 1. Le troisième chapitre se concentre sur l'équirépartition de Zeckendorf et la somme des chiffres des entiers friables dans des classes de congruence. Un entier est dit ( y )-friable si tous ses facteurs premiers sont inférieurs ou égaux à ( y ). Nous utiliserons systématiquement la notation ( P(n) ) pour désigner le plus grand facteur premier de ( n ), et ( S(x, y) := { n leq x : P(n) leq y } ) pour désigner l'ensemble des entiers ( y )-friables inférieurs ou égaux à ( x ). L'objectif principal de ce chapitre est d'évaluer l'ensemble ( { n in S(x, y) : s_varphi(n) equiv a pmod{m} } ), où ( a in mathbb{Z} ) et ( m ) désigne un entier naturel supérieur ou égal à 2. Ici, ( s_varphi ) est la fonction de la somme des chiffres en base Fibonacci. Comme nous le faisons dans le deuxième chapitre, pour prouver le résultat principal, nous utilisons les sommes exponentielles, ainsi, nous profiterons de la propriété de décomposition des entiers friables dans des intervalles pour nos démonstrations afin d'évaluer la somme exponentielle(sum_{n in S(x, y)} e(vartheta s_varphi(n))), où ( vartheta in mathbb{R} setminus mathbb{Z} ). Le quatrième chapitre porte sur la moyenne des sommes de certaines fonctions multiplicatives sur les entiers friables. Dans ce chapitre notre objectif est de déterminer des estimations pour les expressions suivantes : sigma_s(n) = sum_{d mid n} d^s, varphi(n) = sum_{d mid n} mu(d) n/d, et psi(n) = sum_{d mid n} mu^2(n/d) d, où ( s ) est un nombre réel non nul, lorsque n parcourt l'ensemble S(x,y). Le dernier chapitre présente une application de l'inégalité de Turán-Kubilius. Il est bien connu que cette inégalité traite des fonctions additives et qu'elle a également permis de démontrer le théorème de Hardy-Ramanujan pour la fonction additive (omega(n)), qui compte les diviseurs premiers de l'entier (n). Dans ce chapitre, nous nous déplaçons dans l'espace des entiers friables et nous nous intéressons à la fonction additive ilde{omega}(n) = sum_{p mid n atop{s_q(p) equiv a pmod{b}}} 1,où ( a in mathbb{Z} ) et ( b geq 2 ) sont des entiers. Nous fournissons une estimation de (ilde{omega}(n)), lorsque (n) parcourt l'ensemble (S(x,y)), puis nous utilisons l'inégalité de Turán-Kubilius dans l'espace des entiers friables proposée par Tenenbaum et de la Bretèche, et présentons quelques applications
This thesis addresses some questions related to the sum of digits function and friable integers. The first chapter is dedicated to an introduction that gathers the origins of the main topics covered in this thesis, as well as a background and the necessary notations for the rest of the work. The main results obtained during this research will also be presented. The second chapter focuses on the behaviour of the set ({ n leq x : n ext{ is } k ext{-free}, , s_q(Q(n)) equiv a pmod{m} }), where ( a in mathbb{Z} ), ( k ), and ( m ) are natural numbers greater than or equal to 2. The function ( s_q ) represents the sum of digits in base ( q ), ( k )-free integers are those not divisible by the ( k )-th power of a prime number, and ( Q ) is a polynomial of degree greater than or equal to 2. To show our main result, we evaluate exponential sums of the type(sum_{n leq x atop{ n ext{ is } k ext{-free}}} e(alpha s_q(Q(n)))), where ( alpha ) is a real number such that ((q - 1)alpha in mathbb{R} setminus mathbb{Z}). In the end, we establish an equidistribution result modulo 1. The third chapter, we focus on the distribution of the Zeckendorf sum of digits over friable integers in congruence classes. An integer is called ( y )-friable if all its prime factors are less than or equal to ( y ). We use the notation ( P(n) ) to denote the largest prime factor of ( n ), and ( S(x, y) := { n leq x : P(n) leq y } ) to denote the set of ( y )-friable integers less than or equal to ( x ). The main objective of this chapter is to evaluate the set ( { n in S(x, y) : s_varphi(n) equiv a pmod{m} } ), where ( a in mathbb{Z} ) and ( m ) is a natural number greater than or equal to 2. Here, ( s_varphi ) is the sum of digits function in the Fibonacci base. As in the second chapter, to prove the main result, we use exponential sums, and we utilize the property of decomposition of friable integers into intervals for our demonstration to evaluate the exponential sum(sum_{n in S(x, y)} e(vartheta s_varphi(n))), where ( vartheta in mathbb{R} setminus mathbb{Z} ). The fourth chapter deals with the average of sums of certain multiplicative functions over friable integers. In this chapter, our goal is to determine estimates for the following expressions: sigma_s(n) = sum_{d mid n} d^s, varphi(n) = sum_{d mid n} mu(d) n/d, and psi(n) = sum_{d mid n} mu^2(n/d) d, where ( s ) is a non-zero real number, when (n) runs over the set (S(x,y)). The last chapter presents an application of the Turán-Kubilius inequality. It is well known that this inequality deals with additive functions and has also been used to prove the Hardy-Ramanujan theorem for the additive function (omega(n)), which counts the prime divisors of the integer (n). In this chapter, we move into the space of friable integers and focus on the additive function ilde{omega}(n) = sum_{p mid n atop{s_q(p) equiv a pmod{b}}} 1, where ( a in mathbb{Z} ) and ( b geq 2 ) are integers. Firstly, we provide an estimate of ( ilde{omega}(n)) when (n) runs through the set (S(x,y)), we then use the Turán-Kubilius inequality in the space of friable integers established by Tenenbaum and de la Bretèche to present few applications

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6

Reid, W. J. "Experimental investigation of circumferentially non-uniform heat flux on the heat transfer coefficient in a smooth horizontal tube with buoyancy driven secondary flow." Diss., University of Pretoria, 2005. http://hdl.handle.net/2263/66236.

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Most heat transfer tubes are designed for either fully uniform wall temperature or fully uniform wall heat flux boundary conditions under forced convection. Several applications, including but not limited to the solar collectors of renewable energy systems, do however operate with non-uniform boundary conditions. Limited research has been conducted on non-uniform wall heat flux heat transfer coefficients in circular tubes, especially for mixed convection conditions. Such works are normally numerical in nature and little experimental work is available. In this experimental investigation the effects of the circumferential heat flux distribution and heat flux intensity on the single phase (liquid) internal heat transfer coefficient were considered for a horizontal circular tube. Focus was placed on the laminar flow regime of water within a stainless steel tube with an inner diameter of 27.8 mm and a length to diameter ratio of 72. Different outer wall heat flux conditions, including fully uniform and partially uniform heat fluxes were studied for Reynolds numbers ranging from 650 to 2 600 and a Prandtl number range of 4 to 7. The heat flux conditions included 360˚ (uniform) heating, lower 180˚ heating, upper 180˚ heating, 180˚ left and right hemispherical heating, lower 90˚ heating, upper 90˚ heating and slanted 180˚ heating. Depending on the angle span of the heating, local heat fluxes of 6 631 W/m2 , 4 421 W/m2 , 3 316 W/m2 , 2 210 W/m2 and 1 658 W/m2 were applied. Results indicate that the local and average steady state Nusselt numbers are greatly influenced by the applied heat flux position and intensity. Highest average heat transfer coefficients were achieved for case where the applied heat flux was positioned on the lower half (in terms of gravity) of the tubes circumference, while the lowest heat transfer coefficients were achieved when the heating was applied to the upper half of the tube. Variations in the heat transfer coefficient were found to be due to the secondary buoyancy induced flow effect. The relative thermal performance of the different heating scenarios where characterised and described by means of newly developed heat transfer coefficient correlations for fully uniform heating, lower 180° heating, and upper 180° heating.
Dissertation (MEng)--University of Pretoria, 2018.
Mechanical and Aeronautical Engineering
MEng
Unrestricted

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7

Apsilidis, Nikolaos. "Experimental Investigation of Turbulent Flows at Smooth and Rough Wall-Cylinder Junctions." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/71713.

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Junction flows originate from the interaction between a fluid moving over a wall with an obstacle mounted on the same surface. Understanding the physics of such flows is of great interest to engineers responsible for the design of systems consisting of wall-body junctions. From aerodynamics to turbomachinery and electronics to bridge hydraulics, a number of phenomena (drag, heat transfer, scouring) are driven by the behavior of the most prominent feature of junction flows: the horseshoe vortex system (HVS). Focusing on turbulent flows, the complex dynamics of the HVS is established through its unsteadiness and non-uniformity. The fundamentals of this dynamically-rich phenomenon have been described within the body of a rapidly-expanding literature. Nevertheless, important aspects remain inadequately understood and call for further scrutiny. This study emphasized three of them, by investigating the effects of: model scale, wall roughness, and bed geometry. High-resolution experiments were carried out using Particle Image Velocimetry (PIV). Statistical analyses, vortex identification schemes, and Proper Orthogonal decomposition were employed to extract additional information from the large PIV datasets. The time-averaged topology of junction flows developing over a smooth and impermeable wall was independent of the flow Reynolds number, Re (parameter that expresses the effects of scale). On the contrary, time-resolved analysis revealed a trend of increasing vorticity, momentum, and eruptions of near-wall fluid with Re. New insights on the modal dynamics of the HVS were also documented in a modified flow mechanism. Wall roughness (modeled with a permeable layer of crushed stones) diffused turbulence and vorticity throughout the domain. This effect manifested with high levels of intermittency and spatial irregularity for the HVS. Energetic flow structures were also identified away from the typical footprint of the HVS. Finally, a novel implementation of PIV allowed for unique velocity measurements over an erodible bed. It was demonstrated that, during the initial stages of scouring, the downflow at the face of the obstacle becomes the dominant flow characteristic in the absence of the HVS. Notwithstanding modeling limitations, the physical insight contributed here could be used to enhance the design of systems with similar flow and geometrical characteristics.
Ph. D.

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8

Bao, Yanyao. "Smoothed Particle Hydrodynamics Simulations for Dynamic Capillary Interactions." Thesis, The University of Sydney, 2018. http://hdl.handle.net/2123/19592.

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Complex interactions in porous media play an important role on many industrial and geotechnical applications, such as groundwater treatment, porous catalysts, carbon geosequestration, and oil recovery. Rate-dependent wetting effects are of great significance in understanding the multiphase behaviours of porous media thus further throw light on engineering solutions to the above problems. In this thesis, a modified smoothed particle hydrodynamics (SPH) model is applied to simulate (1) the contact angle dynamics and (2) stretching of liquid bridge at meso-scale. This SPH model adopted an inter-particle force formulation with short-range repulsive force and long-range attractive force to take into account single-phase and multiphase interactions. Particularly, a newly-introduced viscous force is imposed at the liquid-solid interface to capture the rate-dependent behaviours of contact angle without prescribing additional arbitrary condition or force. After identification of model parameters, the rate-dependent contact angle behaviours are studied for both wetting and dewetting phenomena. By analysing the contact angle results of fluid at triple-line region with different moving speeds, the dynamic contact angles and corresponding capillary numbers can be correlated by power law functions. The derived correlation and constants are compared with different forms of empirical power law functions and the results are satisfactory. Moreover, we investigated the properties of stretching liquid bridges, including shape evolution, liquid transfer ratio and flow condition under dynamic loading. Different stretching rates are applied, and the shapes of liquid bridge at same breakup distance is presented. By differentiating the wettability of top and bottom substrates, the liquid transfer ratio regarding wettability difference and substrate moving speed is studied.

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9

Hörmann, Wolfgang, and Onur Bayar. "Modelling Probability Distributions from Data and its Influence on Simulation." Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, 2000. http://epub.wu.ac.at/612/1/document.pdf.

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Generating random variates as generalisation of a given sample is an important task for stochastic simulations. The three main methods suggested in the literature are: fitting a standard distribution, constructing an empirical distribution that approximates the cumulative distribution function and generating variates from the kernel density estimate of the data. The last method is practically unknown in the simulation literature although it is as simple as the other two methods. The comparison of the theoretical performance of the methods and the results of three small simulation studies show that a variance corrected version of kernel density estimation performs best and should be used for generating variates directly from a sample. (author's abstract)
Series: Preprint Series / Department of Applied Statistics and Data Processing

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10

Barajas, Leandro G. "Process Control in High-Noise Environments Using A Limited Number Of Measurements." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/7741.

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The topic of this dissertation is the derivation, development, and evaluation of novel hybrid algorithms for process control that use a limited number of measurements and that are suitable to operate in the presence of large amounts of process noise. As an initial step, affine and neural network statistical process models are developed in order to simulate the steady-state system behavior. Such models are vitally important in the evaluation, testing, and improvement of all other process controllers referred to in this work. Afterwards, fuzzy logic controller rules are assimilated into a mathematical characterization of a model that includes the modes and mode transition rules that define a hybrid hierarchical process control. The main processing entity in such framework is a closed-loop control algorithm that performs global and then local optimizations in order to asymptotically reach minimum bias error; this is done while requiring a minimum number of iterations in order to promptly reach a desired operational window. The results of this research are applied to surface mount technology manufacturing-lines yield optimization. This work achieves a practical degree of control over the solder-paste volume deposition in the Stencil Printing Process (SPP). Results show that it is possible to change the operating point of the process by modifying certain machine parameters and even compensate for the difference in height due to change in print direction.

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Книги з теми "Smooth numbers"

1

Sarpkaya, Turgut. In-line and transverse forces on smooth and rough cylinders in oscillatory flow at high Reynolds numbers. Monterey, Calif: Naval Postgraduate School, 1986.

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2

R, Meyer Robert, and Dryden Flight Research Facility, eds. Effects of wing sweep on boundary-layer transition for a smooth F-14A wing at Mach numbers from 0.700 to 0.825. Edwards, Calif: National Aeronautics and Space Administration, Ames Research Center, Dryden Flight Research Facility, 1990.

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3

Sabinin, Lev V. Smooth Quasigroups and Loops. Dordrecht: Springer Netherlands, 1999.

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4

Powers, Sheryll Goecke. Flight wing surface pressure and boundary-layer data report from the F-111 smooth variable-camber supercritical mission adaptive wing. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1997.

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5

Powers, Sheryll Goecke. Flight wing surface pressure and boundary-layer data report from the F-111 smooth variable-camber supercritical mission adaptive wing. [Washington, D.C.]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1997.

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6

H, Hathaway David, Reichmann Edwin J, and George C. Marshall Space Flight Center., eds. On the correlation between maximum amplitude and smoothed monthly mean sunspot number during the rise of the cycle (from t=0-48 months past sunspot minimum). [Marshall Space Flight Center, Ala.]: National Aeronautics and Space Administration, Marshall Space Flight Center, 1998.

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7

Wilson, Robert M. On the correlation between maximum amplitude and smoothed monthly mean sunspot number during the rise of the cycle: From t=0-48 months past sunspot minimum. Linthicum Heights, MD: NASA Center for AeroSpace Information, 1998.

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8

H, Hathaway David, Reichmann Edwin J, and George C. Marshall Space Flight Center., eds. On the correlation between maximum amplitude and smoothed monthly mean sunspot number during the rise of the cycle (from t=0-48 months past sunspot minimum). [Marshall Space Flight Center, Ala.]: National Aeronautics and Space Administration, Marshall Space Flight Center, 1998.

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9

PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics (2011 Messina, Italy). Fractal geometry and dynamical systems in pure and applied mathematics. Edited by Carfi David 1971-, Lapidus, Michel L. (Michel Laurent), 1956-, Pearse, Erin P. J., 1975-, Van Frankenhuysen Machiel 1967-, and Mandelbrot Benoit B. Providence, Rhode Island: American Mathematical Society, 2013.

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10

Dlreah, M. Smooth Sailing Blood Pressure Diary: A 52 Week Tracker to Help Keep Heart Rate, Blood Pressure Systolic and Diastolic Numbers. Independently Published, 2020.

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Частини книг з теми "Smooth numbers"

1

Shiu, Peter. "Smooth Numbers." In Springer Undergraduate Mathematics Series, 349–70. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-63814-5_13.

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2

Felsager, Bjørn. "Smooth Maps—Winding Numbers." In Geometry, Particles, and Fields, 534–613. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0631-6_10.

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3

Jevtić, Filip D. "Smooth Numbers in Music and Architecture." In Zbornik radova / Matematički institut SANU, 69–74. Belgrade: Matematički institut SANU, 2024. http://dx.doi.org/10.18485/mi_sanu_zr.2024.29.21.ch4.

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4

Pomerance, Carl. "The Role of Smooth Numbers in Number Theoretic Algorithms." In Proceedings of the International Congress of Mathematicians, 411–22. Basel: Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9078-6_34.

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5

Aluffi, Paolo. "The characteristic numbers of smooth plane cubics." In Algebraic Geometry Sundance 1986, 1–8. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0082905.

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6

Klocker, Benedikt, Herbert Fleischner, and Günther R. Raidl. "Finding Smooth Graphs with Small Independence Numbers." In Lecture Notes in Computer Science, 527–39. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-72926-8_44.

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7

Sorenson, Jonathan P. "A Fast Algorithm for Approximately Counting Smooth Numbers." In Lecture Notes in Computer Science, 539–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/10722028_36.

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8

Parsell, Scott T., and Jonathan P. Sorenson. "Fast Bounds on the Distribution of Smooth Numbers." In Lecture Notes in Computer Science, 168–81. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11792086_13.

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9

Soundararajan, Kannan. "The distribution of smooth numbers in arithmetic progressions." In CRM Proceedings and Lecture Notes, 115–28. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/crmp/046/08.

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10

Göttsche, Lothar. "Computation of the Betti numbers of Hilbert schemes." In Hilbert Schemes of Zero-Dimensional Subschemes of Smooth Varieties, 12–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0073493.

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Тези доповідей конференцій з теми "Smooth numbers"

1

Huang, Shan, and Neil Kitney. "Model Test on Drag of Cylinders With Helical Grooves at High Reynolds Numbers." In ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/omae2010-20113.

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Towing tank model tests at high Reynolds numbers, up to 1.1×106, were carried out in order to investigate the effects of the triple-starting helical grooves on drag reduction of smooth and rough circular cylinders in uniform cross flow. In total, four cylinders were tested including smooth and rough cylinders with and without helical grooves.

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2

Moon, H. K., T. O’Connell, and R. Sharma. "Heat Transfer Enhancement Using a Convex-Patterned Surface." In ASME Turbo Expo 2002: Power for Land, Sea, and Air. ASMEDC, 2002. http://dx.doi.org/10.1115/gt2002-30476.

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The heat transfer rate from a smooth wall in an internal cooling passage can be significantly enhanced by using a convex patterned surface on the opposite wall of the passage. This design is particularly effective for a design that requires the heat transfer surface to be free of any augmenting features (smooth). Heat transfer coefficients on the smooth wall in a rectangular channel, which had convexities on the opposite wall were experimentally investigated. Friction factors were also measured to assess the thermal performance. Relative clearances (δ/d) between the convexities and the smooth wall of 0, 0.024, and 0.055 were investigated in a Reynolds number (ReHD) range from 15,000 to 35,000. The heat transfer coefficients were measured in the thermally developed region using a transient thermochromic liquid crystal technique. The clearance gap between the convexities and the smooth wall adversely affected the heat transfer enhancement (NuHD). The friction factors (f), measured in the aerodynamically developed region, were largest for the cases of no clearance (δ/d = 0). The average heat transfer enhancement (NuHD) was also largest for the cases of no clearance (δ/d = 0), as high as 3.08 times at a Reynolds number of 11,456 in relative to that (Nuo) of an entirely smooth channel. The normalized Nusselt numbers (NuHD/Nuo), as well as the normalized friction factors (f/fo), for all three cases, decreased with Reynolds numbers. However, the decay rate of the friction factor ratios (f/fo) with Reynolds numbers was lower than that of the normalized Nusselt numbers. For all three cases investigated, the thermal performance ((NuHD/Nuo) /(f/fo)1/3) values were within 5% to each other. The heat transfer enhancement using a convex patterned surface was thermally more effective at a relatively low Reynolds numbers (less than 20,000 for δ/d = 0) than that of a smooth channel.

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3

Eaddy, M., W. H. Melbourne, and J. Sheridan. "Surface Roughness Effects on Circular Cylinders at High Reynolds Numbers." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-32160.

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The problem of flow-induced vibration has been studied extensively. However, much of this research has focused on the smooth cylinder to gain an understanding of the mechanisms that cause vortex-induced vibration. In this paper results of an investigation of the effect of surface roughness on the cross-wind forces are presented. Measurements of the sectional RMS fluctuating lift forces and the axial correlation of the pressures for Reynolds numbers from 1 × 105 to 1.4 × 106 are given. It was found that surface roughness significantly increased the axial correlation of the pressures to similar values found at high subcritical Reynolds numbers. There was little effect of the surface roughness on the sectional lift forces. The improved correlation of the vortex shedding means rough cylinders will be subject to larger cross-wind forces and an increased possibility of vortex-induced vibration compared to smooth cylinders.

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4

De Giorgi, Luigi, Volfango Bertola, Emilio Cafaro, Carlo Cima, Mario De Salve, and Bruno Panella. "Heat Transfer From Liquid Nitrogen Flows in Smooth Pipes." In 2010 14th International Heat Transfer Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ihtc14-22897.

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Convective heat transfer for subcooled liquid nitrogen in a smooth horizontal pipe with internal sources is studied by analytical and numerical methods. For high Reynolds numbers the numerical results are in good agreement with standard heat transfer correlations. At smaller Reynolds numbers (<10,000), large circumferential and longitudinal temperature distributions can observed. The effect of localized heat sources on the heat transfer process is also investigated to simulate insulation failures in cryogenic pipelines. Results show that the presence of constant heat sources is detrimental to the heat transfer from both laminar and turbulent flows.

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5

Allen, Don W., Dean L. Henning, and Li Lee. "Vortex Induced Vibration Tests of Smooth and Rough Flexible Cylinders at High Reynolds Numbers." In ASME 2005 Fluids Engineering Division Summer Meeting. ASMEDC, 2005. http://dx.doi.org/10.1115/fedsm2005-77176.

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Vortex-induced vibration (VIV) tests have been performed on long, flexible pipes with various levels of roughness, in sheared flows in a circular towing tank at high Reynolds numbers. The test pipes, made of fiberglass composite, were mounted horizontally beneath a rotating arm that has a span of 129 ft, and a width of 25 ft. As the towing bridge rotates, it drives the cylinder in a circular path in still water. The sheared flows experienced by the cylinder excite its VIV motion. The Reynolds numbers for the tests reported herein ranged from 152,000 to 339,000 at the high-speed end of the pipe. Two surface roughness levels were tested: one comprised of the exterior surface of a filament wound fiberglass pipe; and one with carpet glued to the exterior of the pipe. The VIV responses of the test cylinders, represented by displacement time traces, spectrum, and motion trajectories, are presented in this paper. Effects of the surface roughness and Reynolds numbers on the VIV responses are discussed. The response behavior of the cylinders varied from single-mode dominance to multi-mode responses, in addition to certain traveling wave activities. These results should be of interest to researchers and engineers in the area of vortex-induced vibrations.

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6

Gao, Haiyang, Hui Hu, and Z. J. Wang. "Computational Study of Unsteady Flows around Dragonfly and Smooth Airfoils at Low Reynolds Numbers." In 46th AIAA Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2008. http://dx.doi.org/10.2514/6.2008-385.

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7

Özen, Ercan, and Mehmet Niyazi Çankaya. "Estimation Of The Turkish Stock Investor Numbers Based On Kernel Method." In 27th International Scientific Conference “Competitiveness and Innovation in the Knowledge Economy”. Academy of Economic Studies of Moldova, 2024. http://dx.doi.org/10.53486/cike2023.47.

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The investigation of investments in stock markets is an important and a challenging topic. Knowing the number of Turkish stock investor makes a benefit to conduct a smooth economical circulation. In this study, it is aimed that the Turkish stock investor numbers are estimated by using the kernel estimation method. The built functions in the Mathematica software are used. The built functions are responsible to model the data sets smoothly. After necessary components of the statistical results in the built function, the random number generation is performed for the estimated function,̂, which is the sampling form of the assumed function 𝑓 for the population representing the investor numbers. The numbers are estimated to be around 5 million for the real data sets if the maximum order statistics are used. The confidence interval as a covering probability being %95 in the asymptotic theory shows that the estimated value can be around 7 million if the new population occurs.

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8

Childs, Dara W., Bassem Kheireddin, and Stephen Phillips. "Friction Factor Behavior From Flat-Plate Tests of Smooth and Hole-Pattern Roughened Surfaces With Supply Pressures up to 84 Bars." In ASME Turbo Expo 2010: Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-22227.

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A flat-plate tester was used to measure the friction-factor behavior for a hole-pattern-roughened surface apposed to a smooth surface. The tests were executed to characterize the friction-factor behavior of annular seals that use a roughened-surface stator and a smooth rotor. Friction factors were obtained from measurements of the mass flow rate and static pressure measurements along the smooth and roughened surfaces. In addition, dynamic pressure measurements were made at four axial locations at the bottom of individual holes and at facing locations in the smooth plate. The test facility is described, and a procedure for determining the friction factor is reviewed. Three clearances were investigated: 0.635, 0.381, and 0.254 mm. Tests were conducted with air at three different inlet pressures (84, 70, and 55 bars), producing a Reynolds numbers range from 50,000 to 700,000. Three surface configurations were tested including smooth-on-smooth, smooth-on-hole, and hole-on-hole. The hole-pattern plates are identical with the exception of the hole depth. For the smooth-on-smooth and smooth-on-hole configurations, the friction factor remains largely constant or increases slightly with increasing Reynolds numbers. The friction factor increases as the clearance between the plates increases. The test program was initiated to investigate a “friction-factor jump” phenomenon cited by Ha et al. in 1992 in test results from a flat-plate tester where, at elevated values of Reynolds numbers, the friction-factor began to increase steadily with increasing Reynolds numbers. They tested apposed honeycomb surfaces. For the present tests, the phenomenon was also observed for tests of apposed roughened surfaces but was not observed for smooth-on-smooth or smooth-on-rough configurations. When the phenomenon was observed, dynamic pressure measurements showed a peak-pressure oscillation at the calculated Helmholtz frequency of the holes.

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9

Zadeh, Shobeir Aliasghar, and Rolf Radespiel. "Turbulence Model Investigation of Water Flow in Rough Micro Channels." In ASME 2009 Fluids Engineering Division Summer Meeting. ASMEDC, 2009. http://dx.doi.org/10.1115/fedsm2009-78190.

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Three-dimensional laminar and turbulent water flows in smooth and rough micro channels with rectangular cross-section were numerically simulated. The hydraulic diameter of the smooth micro channel is 190 μm and 191 μm for the rough one. The roughness inducing surfaces, which were modelled by three rectangular elements placed on the sidewall of the micro channel, are 50 μm high and 50 μm wide. The simulations were conducted for Reynolds numbers between 100 and 4000. The effects on the friction factor and flow characteristics due to the roughness elements, varying Reynolds numbers and low-Reynolds number turbulence models were investigated and compared with the experimental values reported by Hao et al. [1]. Furthermore, the velocity profiles in various Reynolds number and flow regimes have been compared with μPIV measurements. At Reynolds numbers less than 2100 the computed friction factors in the smooth micro channel agree well with the measurements and the values of the conventional theory. For the micro channel with roughness elements, the friction factor approaches the value of measurements and conventional theory, when Re < 900. Transition from laminar to turbulent flow occurs at about Reynolds numbers of 2100 and 900 in smooth and rough micro channel, respectively. Comparison of simulated results using the Spalart-Allmaras and SST K-ω turbulence models with experimental values show good agreement. By contrast, the K-ε model overestimates the pressure loss in micro channels.

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10

Kunkel, Gary J., and Ivan Marusic. "Similarity Formulations for Turbulent Boundary Layers at High Reynolds Numbers." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45455.

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Data obtained from the high Reynolds number atmospheric boundary layer are used to analyze existing mean-flow and turbulence intensity similarity formulations. From the results of this analysis a new streamwise turbulence intensity formulation is proposed that is suggested to be applicable across the entire smooth-wall high Reynolds number turbulent boundary layer. The new formulation is also shown to be consistent with the mixed-flow scaling suggested by other studies.

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Звіти організацій з теми "Smooth numbers"

1

Sánchez-Páez, David A. Effects of income inequality on COVID-19 infections and deaths during the first wave of the pandemic: Evidence from European countries. Verlag der Österreichischen Akademie der Wissenschaften, August 2021. http://dx.doi.org/10.1553/populationyearbook2022.res1.1.

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Evidence from research on infectious diseases suggests that income inequality is related to higher rates of infection and death in disadvantaged population groups. Our objective is to examine whether there was an association between income inequality and the numbers of cases and deaths during the first wave of the COVID- 19 pandemic in European countries. We determined the duration of the first wave by first smoothing the number of daily cases, and then using a LOESS regression to fit the smoothed trend. Next, we estimated quasi-Poisson regressions. Results from the bivariate models suggest there was a moderate positive association between the Gini index values and the cumulated number of infections and deaths during the first wave, although the statistical significance of this association disappeared when controls were included. Results from multivariate models suggest that higher numbers of infections and deaths from COVID-19 were associated with countries having more essential workers, larger elderly populations and lower health care capacities.

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2

Becker, Chris, Anny Francis, Calebe de Roure, and Brendan Wilson. Demand in the Repo Market: Indirect Perspectives from Open Market Operations from 2006 to 2020. Reserve Bank of Australia, May 2024. http://dx.doi.org/10.47688/rdp2024-03.

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In Australia repurchase (repo) obligations are traded bilaterally 'over-the-counter' between parties, rather than on an exchange. As a result, it is difficult to obtain quotes of executable prices, trading volumes, and related data that are representative of the market. Market conditions are therefore not easy to assess and often dependent on anecdotal evidence. Over the years, the Reserve Bank of Australia has published data and analysis of the repo market by providing indirect perspectives using data from its own open market operations that are conducted using repos. This paper contributes to this work. The Reserve Bank conducts open market operations to manage liquidity in the interbank market, provide settlement balances for the smooth functioning of the payments system, and for the implementation of monetary policy. Repos are an integral part of these operations. The eligible private sector counterparties in these auctions have a variety of reasons for participating. We arrange their bids in an ascending order in a number of distinct phases so that they can be used to make inferences about the demand for repo and hence market operations. Several insights allow us to better understand the dynamics underpinning the repo market. The findings mainly relate to the period prior to the implementation of unconventional monetary policies in March 2020.

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3

Zhu, Minjie, and Michael Scott. Two-Dimensional Debris-Fluid-Structure Interaction with the Particle Finite Element Method. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA, April 2024. http://dx.doi.org/10.55461/gsfh8371.

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In addition to tsunami wave loading, tsunami-driven debris can cause significant damage to coastal infrastructure and critical bridge lifelines. Using numerical simulations to predict loads imparted by debris on structures is necessary to supplement the limited number of physical experiments of in-water debris loading. To supplement SPH-FEM (Smoothed Particle Hydrodynamics-Finite Element Method) simulations described in a companion PEER report, fluid-structure-debris simulations using the Particle Finite Element Method (PFEM) show the debris modeling capabilities in OpenSees. A new contact element simulates solid to solid interaction with the PFEM. Two-dimensional simulations are compared to physical experiments conducted in the Oregon State University Large Wave Flume by other researchers and the formulations are extended to three-dimensional analysis. Computational times are reported to compare the PFEM simulations with other numerical methods of modeling fluid-structure interaction (FSI) with debris. The FSI and debris simulation capabilities complement the widely used structural and geotechnical earthquake simulation capabilities of OpenSees and establish the foundation for multi-hazard earthquake and tsunami simulation to include debris.

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4

Schuurman, Gregor, Amber Runyon, Brecken Robb, Morris Hylton, and Jeneva Wright. Resource stewardship objectives and actions for climate change-sensitive cultural and natural resources in Wrangell-St. Elias National Park and Preserve: Outputs from January?February 2022 climate change adaptation strategy development. National Park Service, 2024. http://dx.doi.org/10.36967/2301930.

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This report presents climate change-informed resource stewardship strategies for diverse Wrangell-St. Elias National Park and Preserve natural and cultural resources. The strategies were developed in early 2022 by park staff and other subject-matter experts in a scenario-based climate change adaptation planning process. Strategy development was facilitated by National Park Service (NPS) climate change adaptation specialists. Strategies address critical climate change implications for park resources identified in an immediately preceding (fall-2021) climate-resource scenario development process. The overall, nearly-year-long scenario- and strategy-development process was entirely virtual due to the COVID-19 pandemic. Although this circumstance was constraining in some ways, it also provided many benefits, including lower barriers to participant entry, smoother pacing, more opportunities to incorporate personal reflection and individual work, and more points in the process where facilitators could intervene to support participants or make changes. Absence of travel costs, plus organization of the process into a larger number of smaller steps than in the past, allowed the 11 participating park resource management staff to include a large pool of several dozen federal, tribal, state, academic, and private-sector partners. Climate change adaptation strategies are most likely to foster climate change-informed resource stewardship when they support a specific planning process. In this case, that process was the 2021?2023 development of the Wrangell-St. Elias National Park and Preserve Resource Stewardship Strategy. A Resource Stewardship Strategy is a dynamic planning tool that parks use to set goals for natural and cultural resource stewardship, identify activities to achieve and maintain desired conditions, and track progress.

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5

Monge-González, Ricardo, and Federico Torres-Carballo. The Dynamics of Entrepreneurship in Costa Rica: An Analysis of Firm Entry, Exit, and Growth Rates. Inter-American Development Bank, January 2015. http://dx.doi.org/10.18235/0006994.

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This study explores for the first time the dynamics of entrepreneurship in Costa Rica based on an analysis of firm entry, exit, and growth rates. Using panel data from 2001 to 2012, it explores the extent to which the growth rates of firms are independent of firm size (Gibrat's law), controlling for age and other possible determinants of growth rates. It also analyzes the question of whether Costa Rica is suffering from the missing middle phenomenon. In addition, it explores the questions of which firms are generating more jobs and which companies show high and sustained growth rates (gazelles). The results show an inverse relationship between size and growth rates of firms, even after controlling for age, which does not agree with the predictions of Gibrat's law. In short, it was found that young and small firms are growing faster than older and larger firms in Costa Rica. However, the results also show that large firms are the only ones whose average size increased between 2001 and 2012. It is clear that Costa Rica is not suffering from the missing middle phenomenon, because although there are a very large number of micro and small firms, there is not a bimodal distribution. Indeed, mid-sized firms are missing, but large firms are missing too, and the fraction of firms of a given size is smoothly declining in firm size in all of the years analyzed. On the other hand, a positive and significant relationship between the growth rates of firms and their export experience was found, as well as between the former and firm participation as a local supplier of multinational companies.

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6

Olsson, Olle. Industrial decarbonization done right: identifying success factors for well-functioning permitting processes. Stockholm Environment Institute, November 2021. http://dx.doi.org/10.51414/sei2021.034.

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1 Introduction 1.1 The urgency of industrial decarbonization The last few years have seen several of the world’s largest carbon dioxide-emitting countries and leading heavy industry companies committing to mid-century net-zero targets (Buckley 2021; Denyer and Kashiwagi 2020; McCurry 2020; Myers 2020). Consequently, the discussion on economy-wide transition to net-zero is accelerating, with focus shifting from “if” to “when” and “how”, even for heavy industry sectors like steel, cement and chemicals. This makes it increasingly urgent to analyse not just whether it is technologically feasible to decarbonize heavy industry, but also investigate issues more directly related to practical implementation. This includes site-specific planning, infrastructure availability, and consultation with local authorities and other stakeholders. Many of the latter considerations are formalized as part of the permitting processes that are an essential vehicle to ensure that industrial interests are balanced against interests of society at large. However, doing this balancing act can turn out to be very complicated and associated with uncertainties as to their outcome, as well as being demanding in resources and time. At the same time, to ensure broad buy-in and support from society, the investments needed must be implemented in a way that takes a broad spectrum of sustainability concerns into account, not just climate change mitigation. A key question is if and how permitting processes can run more smoothly and efficiently while still ensuring inclusive consultations, fair procedures and adherence to legal certainty. This policy brief discusses this question from the starting point of Swedish conditions, but many of the points raised will be relevant for a broader international discussion on taking industrial decarbonization to implementation. 1.2 Industrial transition and permitting processes in Sweden Decarbonization of the industrial sector in Sweden essentially entails a relatively small number of investment projects in the cement, steel, petrochemical and refinery sectors, where the vast majority of carbon emissions are concentrated (Karltorp et al. 2019; Nykvist et al. 2020). However, while few in number, the size of these investments means that their implementation will by necessity become relevant to many other parts of society. In connection with the increasing focus on how to implement industrial decarbonization in Sweden, discussions about permitting processes have been brought higher up on the agenda. While there has been an active discussion on permitting processes in Sweden for quite some time, it has primarily been focused on aspects related to mining and wind power (Larsen et al. 2017; Raitio et al. 2020). The last few years have, however, focused increasingly on industrial projects, in particular related to a proposed – though eventually cancelled – expansion of an oil refinery in the southwestern part of the country (Blad 2020). In terms of political discussions, both the governmental initiative Fossil-free Sweden (2020) and the Swedish Climate Policy Council (2020) emphasize that permitting processes need to become faster in order for Sweden’s industrial transition to be implemented in line with the time plan set by the 2017 Swedish Climate Act. Business representatives and organizations are also voicing concerns about the slow speed of permitting (Balanskommissionen 2019; Jacke 2018). At the same time, criticism has been raised that much of the environmental damage done in Sweden comes from activities conducted within limits set by environmental permits, which could be a flaw in the system (Malmaeus and Lindblom 2019). Finally, recent public inquiries have also discussed permitting processes.

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7

Kimhi, Ayal, Barry Goodwin, Ashok Mishra, Avner Ahituv, and Yoav Kislev. The dynamics of off-farm employment, farm size, and farm structure. United States Department of Agriculture, September 2006. http://dx.doi.org/10.32747/2006.7695877.bard.

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Objectives: (1) Preparing panel data sets for both the United States and Israel that contain a rich set of farm attributes, such as size, specialization, and output composition, and farmers’ characteristics such as off-farm employment status, education, and family composition. (2) Developing an empirical framework for the joint analysis of all the endogenous variables of interest in a dynamic setting. (3) Estimating simultaneous equations of the endogenous variables using the panel data sets from both countries. (4) Analyzing, using the empirical results, the possible effects of economic policies and institutional changes on the dynamics of the farm sector. An added objective is analyzing structural changes in farm sectors in additional countries. Background: Farm sectors in developed countries, including the U.S. and Israel, have experienced a sharp decline in their size and importance during the second half of the 20th century. The overall trend is towards fewer and larger farms that rely less on family labor. These structural changes have been a reaction to changes in technology, in government policies, and in market conditions: decreasing terms of trade, increasing alternative opportunities, and urbanization pressures. As these factors continue to change, so does the structure of the agricultural sector. Conclusions: We have shown that all major dimensions of structural changes in agriculture are closely interlinked. These include farm efficiency, farm scale, farm scope (diversification), and off-farm labor. We have also shown that these conclusions hold and perhaps even become stronger whenever dynamic aspects of structural adjustments are explicitly modeled using longitudinal data. While the results vary somewhat in the different applications, several common features are observed for both the U.S. and Israel. First, the trend towards the concentration of farm production in a smaller number of larger farm enterprises is likely to continue. Second, at the micro level, increased farm size is negatively associated with increased off-farm labor, with the causality going both ways. Third, the increase in farm size is mostly achieved by diversifying farm production into additional activities (crops or livestock). All these imply that the farm sector converges towards a bi-modal farm distribution, with some farms becoming commercial while the remaining farm households either exit farming altogether or continue producing but rely heavily on off-farm income. Implications: The primary scientific implication of this project is that one should not analyze a specific farm attribute in isolation. We have shown that controlling for the joint determination of the various farm and household attributes is crucial for obtaining meaningful empirical results. The policy implications are to some extent general but could be different in the two countries. The general implication is that farm policy is an important determinant of structural changes in the farm sector. For the U.S., we have shown the different effects of coupled and decoupled (direct) farm payments on the various farm attributes, and also shown that it is important to take into account the joint farm-household decisions in order to conduct a meaningful policy analysis. Only this kind of analysis explains the indirect effect of direct farm payments on farm production decisions. For Israel, we concluded that farm policy (or lack of farm policy) has contributed to the fast structural changes we observed over the last 25 years. The sharp change of direction in farm policy that started in the early 1980s has accelerated structural changes that could have been smoother otherwise. These accelerated structural changes most likely lead to welfare losses in rural areas.

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8

Independent Consultation and Investigation Mechanism: 2013 Annual Report. Inter-American Development Bank, May 2014. http://dx.doi.org/10.18235/0005888.

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The operation of the Independent Consultation and Investigation Mechanism (ICIM) saw the convergence of a number of significant milestones in 2013. Based on the findings and recommendations of an evaluation report by the IDB Office of Evaluation and Oversight (OVE) in 2012, the year began with the decision of the Board OF Executive Directors to initiate a process of adjustment to the ICIM Policy and its operating structure. This work, including the implementation of a process of public consultation, was commissioned to an independent expert.In addition, 2013 marked the end of the ICIMs pilot period. During this period (2010-2013) a total of 76 requests from 9 different countries were received. The 2013 Annual Report contains information on the management of ICIM's active portfolio and is complemented by information on each of the requests in the Public Registry, also newly updated in 2013. Of particular importance during the three years has been the completion of two processes of investigation and the approval of a third for the Compliance Review Phase, and the closing of five cases with agreements in the Consultation Phase. A statistical annex provides the reader with further information on the ICIM portfolio of Requests, the concerns of the Requesters and the sectors that most frequently generate these concerns among communities. In September 2013, and as stated its Policy, the scope of the ICIM was expanded to cover all the Relevant Operational Policies in force. Finally, in order to maintain consistency in the responsiveness of the Mechanism and to ensure a smooth transition once the revised policy is approved, the Board of Executive Directors approved a transition plan related to Mechanisms governance that ensures the continued operation thereof until the new policy goes into effect.

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Financial Stability Report - Second Semester of 2020. Banco de la República de Colombia, March 2021. http://dx.doi.org/10.32468/rept-estab-fin.sem2.eng-2020.

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The Colombian financial system has not suffered major structural disruptions during these months of deep economic contraction and has continued to carry out its basic functions as usual, thus facilitating the economy's response to extreme conditions. This is the result of the soundness of financial institutions at the beginning of the crisis, which was reflected in high liquidity and capital adequacy indicators as well as in the timely response of various authorities. Banco de la República lowered its policy interest rates 250 points to 1.75%, the lowest level since the creation of the new independent bank in 1991, and provided ample temporary and permanent liquidity in both pesos and foreign currency. The Office of the Financial Superintendent of Colombia, in turn, adopted prudential measures to facilitate changes in the conditions for loans in effect and temporary rules for rating and loan-loss provisions. Finally, the national government expanded the transfers as well as the guaranteed credit programs for the economy. The supply of real credit (i.e. discounting inflation) in the economy is 4% higher today than it was 12 months ago with especially marked growth in the housing (5.6%) and commercial (4.7%) loan portfolios (2.3% in consumer and -0.1% in microloans), but there have been significant changes over time. During the first few months of the quarantine, firms increased their demands for liquidity sharply while consumers reduced theirs. Since then, the growth of credit to firms has tended to slow down, while consumer and housing credit has grown. The financial system has responded satisfactorily to the changes in the respective demands of each group or sector and loans may grow at high rates in 2021 if GDP grows at rates close to 4.6% as the technical staff at the Bank expects; but the forecasts are highly uncertain. After the strict quarantine implemented by authorities in Colombia, the turmoil seen in March and early April, which was evident in the sudden reddening of macroeconomic variables on the risk heatmap in Graph A,[1] and the drop in crude oil and coal prices (note the high volatility registered in market risk for the region on Graph A) the local financial markets stabilized relatively quickly. Banco de la República’s credible and sustained policy response played a decisive role in this stabilization in terms of liquidity provision through a sharp expansion of repo operations (and changes in amounts, terms, counterparties, and eligible instruments), the purchases of public and private debt, and the reduction in bank reserve requirements. In this respect, there is now abundant aggregate liquidity and significant improvements in the liquidity position of investment funds. In this context, the main vulnerability factor for financial stability in the short term is still the high degree of uncertainty surrounding loan quality. First, the future trajectory of the number of people infected and deceased by the virus and the possible need for additional health measures is uncertain. For that reason, there is also uncertainty about the path for economic recovery in the short and medium term. Second, the degree to which the current shock will be reflected in loan quality once the risk materializes in banks’ financial statements is uncertain. For the time being, the credit risk heatmap (Graph B) indicates that non-performing and risky loans have not shown major deterioration, but past experience indicates that periods of sharp economic slowdown eventually tend to coincide with rises in non-performing loans: the calculations included in this report suggest that the impact of the recession on credit quality could be significant in the short term. This is particularly worrying since the profitability of credit establishments has been declining in recent months, and this could affect their ability to provide credit to the real sector of the economy. In order to adopt a forward-looking approach to this vulnerability, this Report presents several stress tests that evaluate the resilience of the liquidity and capital adequacy of credit institutions and investment funds in the event of a hypothetical scenario that seeks to simulate an extreme version of current macroeconomic conditions. The results suggest that even though there could be strong impacts on the credit institutions’ volume of credit and profitability under such scenarios, aggregate indicators of total and core capital adequacy will probably remain at levels that are above the regulatory limits over the horizon of a year. At the same time, the exercises highlight the high capacity of the system's liquidity to face adverse scenarios. In compliance with its constitutional objectives and in coordination with the financial system's security network, Banco de la República will continue to closely monitor the outlook for financial stability at this juncture and will make the decisions that are necessary to ensure the proper functioning of the economy, facilitate the flow of sufficient credit and liquidity resources, and further the smooth operation of the payment systems. Juan José Echavarría Governor

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